Metamath Proof Explorer


Theorem 5p3e8

Description: 5 + 3 = 8. (Contributed by NM, 11-May-2004)

Ref Expression
Assertion 5p3e8 5 + 3 = 8

Proof

Step Hyp Ref Expression
1 df-3 3 = 2 + 1
2 1 oveq2i 5 + 3 = 5 + 2 + 1
3 5cn 5
4 2cn 2
5 ax-1cn 1
6 3 4 5 addassi 5 + 2 + 1 = 5 + 2 + 1
7 2 6 eqtr4i 5 + 3 = 5 + 2 + 1
8 df-8 8 = 7 + 1
9 5p2e7 5 + 2 = 7
10 9 oveq1i 5 + 2 + 1 = 7 + 1
11 8 10 eqtr4i 8 = 5 + 2 + 1
12 7 11 eqtr4i 5 + 3 = 8